The prospect for those seeking and hoping to keep jobs last month was mixed in Santa Clara and San Benito counties, according to data released Friday by California’s Employment Development Department.

The two counties saw their seasonally unadjusted unemployment rate hit 5.6 percent, which was up from 5.2 percent in April and 4.4 percent from May 2007.

Still, that was better than the state as a whole. The May seasonally unadjusted unemployment rate was 6.5 percent for California and 5.2 percent for the nation.

And, there was this tidbit of good news: Santa Clara and San Benito counties added 4,600 jobs from April to May.

Leisure and hospitality businesses accounted for 1,400 of those new jobs in Santa Clara and San Benito counties, with food-service employers hiring 900 of them. Professional and businesses services added 900 jobs, and private educational and health services tacked on 700.

Officials with the Employment Development Department said they did not have a comparable seasonally unadjusted figure for the change in the number of jobs statewide from April to May. But using seasonally adjusted data, the state lost 10,900 jobs during that period.

“The last time the unemployment rate in California was this high was in November of 2003 as the long period of job loss after the Internet bubble burst was coming to an end,” said Stephen Levy, director of the Center for Continuing Study of the California Economy in Palo Alto.

“There is no question that the state economy is in a slowdown and that the slowdown will probably last for at least another year, continuing the pressure on state and local government budgets into 2009 and 2010,” Levy added.

A separate employee confidence survey, conducted monthly by Harris Interactive on behalf of staffing and recruiting firm Spherion of Florida, found a slight drop in workers’ optimism statewide. While 73 percent of the workers interviewed said they considered it unlikely they will lose their jobs in the next year, that was a 6 percentage point decrease from April.

Harris declines to give a margin of error for the survey.

It’s unclear from the data why the number of jobs and the unemployment rate both increased in Santa Clara and San Benito counties.

That can happen when the overall number of people in the labor force, including those working as well as those filing for unemployment, increases, said Janice Shriver, a labor market consultant for the state. She speculated that the labor-force population for the two counties might have risen in part because of an increase in people picking strawberries or doing other farm work, but she wasn’t sure.

Nonetheless, Shriver called the 4,600 new jobs “encouraging.”

Levy also found the data curious.

“I’m puzzled by why people are still pouring into the labor force when they know jobs are scarce,” he said.

One reason the unemployment rate looks worse than the number of jobs is that some formerly self-employed people may have decided to quit their businesses. While those people would have caused the unemployment rolls to rise, the self-employed tend to be excluded from the job data, he said.

Whatever the case, Levy saw reason for some optimism for Silicon Valley.

“We’re slowing along with the rest of the state, but still showing positive job growth,” he said. “Whatever is going on now wasn’t what was going on in 2000, when we lost 200,000 jobs.”